Simulation of propagation along a cylindrical bundle of cardiac tissue. I. Mathematical formulation

A mathematical description, based on a three-dimensional model for studying propagation in cardiac muscle is given. The model makes use of the bidomain concept to construct a representation of a cylindrical, multicellular bundle lying in an extensive volume conductor. The equations for the cylindrical bidomain are derived for different combinations of boundary conditions and simplifying assumptions. The analysis shows that an analytic model for propagation can be set up if one assumes that the ratio of the intracellular and interstitial bidomain conductivities in the radial and axial direction are the same (i.e. equal anisotropy) and the intracellular radial current density vanishes at the surface. As a point of reference, the classical one-dimensional cable model is also examined and the expressions governing propagation are reformulated to account for the extracellular medium, a factor ignored in most simulation studies.